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PostPosted: Fri Apr 15, 2011 12:50 am 
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DSMok1



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PostPosted: Wed Jul 14, 2010 4:39 pm Post subject: Advanced Statistical Plus/Minus Reply with quote
Advanced Statistical Plus/Minus

I've been working on deriving a new SPM regression based purely upon "advanced" stats (like TS% and OR%) for some time now. I feel comfortable enough with the results thus far to release the first iteration of this SPM.

The data used: Neil Paine's collection of 1-Yr APM's (unfortunately without std err's; I estimated the standard errors for weighting purposes), Joe Sill's 4 Year RAPM's, with the regression toward 0 backed out, and finally (and most importantly) Steve Ilardi's 6-Year APM's posted on this forum. These 6 Year APM's had quite low errors, and provided the groundwork for this regression. I weighted each player in the regression by 1/stderr^2, where stderr is their APM standard error.

I then compiled the advanced metrics from the Basketball Reference Play Index for each player, and weighted-averaged the multi-year data (including playoffs, for the APM's that included those). Thus I have 3 APM data sets and the associated advanced statistics.

I experimented with a number of constructions for the rebounding and especially the scoring parts of this regression. Finding a good way to relate turnovers, shooting, usage, and assists proved illusive for some time. I finally now have a construction I am comfortable with, though (like with any construction) there are a few holes.

To avoid over-weighting steals and blocks for defense, I also included offensive rating and defensive rating of the teams. This is not included in the final SPM, because the team adjustment (to make the teams sum to their efficiency differentials) already accounts for this.

Here are the factors in this regression:

Code:
Factor Value
TRB% 1.33823090
TRB^2 -0.08918572
TRB^3 0.00219790

STL% 1.43951052
BLK% 0.35237880
MPG 0.10099403

TO% Coeff 0.66920540
PPP Threshold 1.64758151
PPP USG Scale 0.01394727
PPP AST Scale 0.01005596
Scoring 0.55728095
USG Const 4.67604494

Intercept -6.90680060


Let me explain.

First of all, note the rebounding terms. I discovered that the value of splitting rebounding into offensive and defensive was much less than that of adding this nonlinearity (which didn't work when ORB and DRB were split). Basically, in the neighborhood of 10%, there isn't a huge amount of change. A player that gets very few rebound hurts the team a lot, and a player near 20% rebounds helps quite a bit. Here's a quick table:

Code:
TRB% Pts
0 0.00
2.5 2.82
5 4.74
7.5 5.95
10 6.66
12.5 7.09
15 7.42
17.5 7.89
20 8.67
22.5 10.00
25 12.06


Next: steals, blocks and MPG. These are all straightforward, linear terms. Be aware, though: I'm inputing these percentages throughout in their whole-number forms, like Basketball-Reference outputs them.

Charges taken would be added into the steals term--other research I've done shows them to be equivalent in SPM terms (1 ChgTkn = 1 Steal). I'm trying to make this SPM able to be applied historically; thus I've left that out.

Here's the complicated part: the scoring term. First the actual formula:

Code:
{TS%*2*(1-TO%/100) - TO%Coeff*(TO%/100) - (PPPThreshold - PPPUSGScale*USG% - PPPASTScale*AST%)}*(USG% + USGConst)*Scoring


What's going on here? First of all, this is basically an efficiency*USG term. It takes into account TS%, USG%, TO%, and AST% to create a composite scoring value.

Now, term by term. The True Shooting term is very basic. It gives the number of points scored per possession used by the player. Next, the turnover term provides the penalty for each turnover. These terms make up the efficiency side of the equation.

Next, the PPP (Points per Possession) threshold and modifiers. The threshold is just a baseline constant. Then usage is subtracted out, indicating from the regression that there is a clear benefit to having a higher usage--in fact, .1 PPP per 7 %USG increased. Finally, the assist modifier. This is the ONLY place in the regression that has assists included. It was not significant anywhere else I tried it, compared to this location in the regression. Assists also modify the PPP; when everything is multiplied through the assists basically go to the form AST%*(USG%+Constant), which is a reasonable construction.

Finally, the whole (PPP - PPPThreshold) term is multiplied by (USG% + USGConst). Again, we're using whole percentages, everywhere but with TS% (I'm following Basketball Reference on this). Because of the USGConst, even if a player has NO usage, he still gets some credit for assists. Just not very much. In other words, Steve Blake just isn't that great.

Finally, after compiling the RAW SPM, the team adjustment must be applied. This can range from negligible (Cleveland, Boston, and Utah had 0 team adjustments this year) to quite large (+1.36 for ORL, -1.43 for GSW). Mostly defense is what is accounted for by the team adjustment since it is not captured well by the regression.

Here is a sample of the results--the top 20 in SPM, minimum 1000 minutes:

Code:
Rnk Tm Player G MP SPM
1 CLE LeBron James 76 2966 12.16
2 MIA Dwyane Wade 77 2792 9.69
3 NOH Chris Paul 45 1712 6.51
4 ORL Dwight Howard 82 2843 6.31
5 SAS Manu Ginobili 75 2150 5.57
6 LAL Kobe Bryant 73 2835 5.38
7 OKC Kevin Durant 82 3239 5.32
8 SAS Tim Duncan 78 2438 5.21
9 BOS Rajon Rondo 81 2963 4.82
10 LAC Marcus Camby 51 1596 4.81
11 UTA Deron Williams 76 2802 4.42
12 ATL Josh Smith 81 2871 4.32
13 DAL Dirk Nowitzki 81 3039 4.07
14 LAL Pau Gasol 65 2403 4.01
15 UTA Carlos Boozer 78 2673 3.99
16 WAS Gilbert Arenas 32 1169 3.90
17 DEN Nene Hilario 82 2755 3.77
18 TOR Chris Bosh 70 2526 3.62
19 CHA Gerald Wallace 76 3119 3.53
20 DEN Carmelo Anthony 69 2634 3.51


The full results for 2009-2010 regular season are here: Google Spreadsheet: Advanced SPM 09-10

EDIT: See later in this thread for revisions to this method and a complete spreadsheet to play with.

Last edited by DSMok1 on Tue Oct 26, 2010 12:11 pm; edited 1 time in total
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Ilardi



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PostPosted: Wed Jul 14, 2010 4:55 pm Post subject: Reply with quote
Nice work, DSM: this looks like an important contribution.

A couple of quick questions:

a) Can you provide standard error (se) estimates for the SPM values?

b) Did you consider using any of the advanced metrics from 82games? I've always thought eFG% Allowed would be quite useful in an SPM model . . .

c) What is the correlation between your SPM values for each player and his corresponding APM value? (i.e., the zero-order correlation for the entire league)

d) Any plans for "out-of-sample testing" on this new SPM metric (a la Joe Sill)?
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DSMok1



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PostPosted: Wed Jul 14, 2010 5:38 pm Post subject: Reply with quote
Ilardi wrote:
Nice work, DSM: this looks like an important contribution.

A couple of quick questions:

a) Can you provide standard error (se) estimates for the SPM values?

b) Did you consider using any of the advanced metrics from 82games? I've always thought eFG% Allowed would be quite useful in an SPM model . . .

c) What is the correlation between your SPM values for each player and his corresponding APM value? (i.e., the zero-order correlation for the entire league)

d) Any plans for "out-of-sample testing" on this new SPM metric (a la Joe Sill)?


Good to see you around, Ilardi!

a) How would I go about developing them for a nonlinear model? I would love to, but haven't figured out how. Another issue with the standard errors is that the APM against which we are regressing has error within it (which I think biases the error on the regression upwards).

b) I wanted to make this metric as useful historically as possible. Basketball Reference has all of the stats used in this regression back to 1977. A more intricate SPM is possible, using things like eFG% allowed, location of assists, etc.

c) I can run that... should I do it just on the low-error six season sample?

d) That would be tough for me to do. I don't have a lot of samples to work with.

Thanks for the input!
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Ilardi



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PostPosted: Wed Jul 14, 2010 6:01 pm Post subject: Reply with quote
Thanks: and most guys on the forum call me 'Steve'.

I'd have to get a consult to figure out how to calculate se's on a nonlinear metric like that, but I know it must be do-able. Perhaps someone on this forum can point the way to a workable approach?

As for the correlation between SPM and APM, I might suggest using the 08-09 season, for which you have my 6-season estimates (weighted heavily toward 08-09), as well as your own SPM values.

On the out-of-sample test: presumably it would be possible to calculate SPM values for each player based on games through, say, the first 4 months of last season, and then use those estimates to predict results of the final 2 months. (Same basic approach Joe used with his ridge regression APM numbers.) It would be a fair amount of work, but should be easily do-able, at least in principle.
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PostPosted: Wed Jul 14, 2010 11:47 pm Post subject: Reply with quote
Ilardi wrote:
Thanks: and most guys on the forum call me 'Steve'.

I'd have to get a consult to figure out how to calculate se's on a nonlinear metric like that, but I know it must be do-able. Perhaps someone on this forum can point the way to a workable approach?

As for the correlation between SPM and APM, I might suggest using the 08-09 season, for which you have my 6-season estimates (weighted heavily toward 08-09), as well as your own SPM values.

On the out-of-sample test: presumably it would be possible to calculate SPM values for each player based on games through, say, the first 4 months of last season, and then use those estimates to predict results of the final 2 months. (Same basic approach Joe used with his ridge regression APM numbers.) It would be a fair amount of work, but should be easily do-able, at least in principle.


I'd love to figure out how to do standard errors on nonlinear metrics.

I'll look into the correlation for the data you suggested, when I have time.

I still have issues with the out of sample test, because it is replacing a descriptive stat with a predictive stat--which is why the ridge regression technique provided the best out-of-sample results. It's basically regression to the mean. When I do regression, I'm going to use the samples, with their error, and regress in a Bayesian manner toward a prior based on peripheral data.
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Ilardi



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PostPosted: Thu Jul 15, 2010 12:18 pm Post subject: Reply with quote
DSMok1 wrote:
I still have issues with the out of sample test, because it is replacing a descriptive stat with a predictive stat--which is why the ridge regression technique provided the best out-of-sample results. It's basically regression to the mean. When I do regression, I'm going to use the samples, with their error, and regress in a Bayesian manner toward a prior based on peripheral data.


But isn't the utility of any metric linked in large part to its predictive ability? Certainly, in the natural sciences, the valid prediction of phenomena is regarded as the sine qua non of the entire enterprise, so I'm admittedly a bit biased, but suffice it to say that even NBA decision makers realize that it's much more valuable to have a stat that gives accurate prediction than one that merely provides accurate description.

Also, although ridge regression makes use of 'regression to the mean', it does so in a limited way - essentially by simply reining in outlier values via an a priori (Bayesian) determination that they are unlikely. In my view, it's an extremely clever technique for enhancing the 'signal' of player APM values via tamping down the 'noise' of extreme variations in efficiency from one low-minute lineup to another.
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PostPosted: Thu Jul 15, 2010 1:00 pm Post subject: Reply with quote
Ilardi wrote:
DSMok1 wrote:
I still have issues with the out of sample test, because it is replacing a descriptive stat with a predictive stat--which is why the ridge regression technique provided the best out-of-sample results. It's basically regression to the mean. When I do regression, I'm going to use the samples, with their error, and regress in a Bayesian manner toward a prior based on peripheral data.


But isn't the utility of any metric linked in large part to its predictive ability? Certainly, in the natural sciences, the valid prediction of phenomena is regarded as the sine qua non of the entire enterprise, so I'm admittedly a bit biased, but suffice it to say that even NBA decision makers realize that it's much more valuable to have a stat that gives accurate prediction than one that merely provides accurate description.

Also, although ridge regression makes use of 'regression to the mean', it does so in a limited way - essentially by simply reining in outlier values via an a priori (Bayesian) determination that they are unlikely. In my view, it's an extremely clever technique for enhancing the 'signal' of player APM values via tamping down the 'noise' of extreme variations in efficiency from one low-minute lineup to another.


I'm not disputing the value of prediction. However, I'd like to do that AFTER the SPM is calculated. In other words, construct a SPM, THEN apply the Bayesian regression to estimate "true talent", then combine with previous years to create a projection. I simply want the SPM itself to not be "biased" with information outside of actual production numbers.

I agree that RAPM works very well, but it does have a few quirks. Like Anderson Varajao getting very highly rated because it is so unlikely that Lebron is really a +11 player.
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Ilardi



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PostPosted: Sat Jul 17, 2010 10:40 am Post subject: Reply with quote
I've also had Varajao rated highly using a more traditional APM approach . . .
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PostPosted: Sat Jul 17, 2010 12:27 pm Post subject: Reply with quote
Ilardi wrote:
I've also had Varajao rated highly using a more traditional APM approach . . .


15th is pretty high. That's what the 4-year RAPM had him. Don't you think there is possibility of using the Bayesian in such a way causing some odd effects like that?

Also--would it be possible to get from you a 4 year, regular season only APM, though 09-10? Then I could use the advanced stats collected by Hoopdata in that time to run a more comprehensive SPM.
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PostPosted: Sat Jul 17, 2010 2:50 pm Post subject: Reply with quote
Great work, DSMok!! I'm trying to replicate your work, and I had a question: how are you doing the team adjustment? What I always did was to find the minute-weighted average of each team's SPM and multiply by 5, then subtract that from the team's actual efficiency differential and divide the result by 5. But when I do that, my team adjustments don't match yours (ORL is +1.26, GSW is -1.70). Is it a rounding issue (I'm using the full, calculated versions of the BBR stats, while you used rounded versions), or is my team adjustment method incorrect?
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DSMok1



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PostPosted: Sat Jul 17, 2010 4:02 pm Post subject: Reply with quote
Neil Paine wrote:
Great work, DSMok!! I'm trying to replicate your work, and I had a question: how are you doing the team adjustment? What I always did was to find the minute-weighted average of each team's SPM and multiply by 5, then subtract that from the team's actual efficiency differential and divide the result by 5. But when I do that, my team adjustments don't match yours (ORL is +1.26, GSW is -1.70). Is it a rounding issue (I'm using the full, calculated versions of the BBR stats, while you used rounded versions), or is my team adjustment method incorrect?


I didn't use the team efficiency precisely. I summed to 2/3 SRS 1/3 Efficiency differential. Is the SRS calculated from efficiency differentials or point margins? If it is calculated off of efficiency differentials per game, it should be the best thing to sum to. I think it's point differential, which is why I used the average I did. But whatever you choose to sum to, that's up to you.

I'm glad you're doing this! You've got all of the data for compiling a full list and actually doing the team adjustments correctly.

I'm hoping this doesn't undervalue great centers--because there weren't any in the time period I used for the regression, I don't know if the top end of the regression can capture them. Then again, I don't know how much a great center truly contributed, either.
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Ilardi



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PostPosted: Sat Jul 17, 2010 4:59 pm Post subject: Reply with quote
[quote="DSMok1"]
Ilardi wrote:

Also--would it be possible to get from you a 4 year, regular season only APM, though 09-10? Then I could use the advanced stats collected by Hoopdata in that time to run a more comprehensive SPM.


I haven't run it yet, but maybe your request will be just the catalyst I need. Is it really the case that no one else out there has put out any publicly available multi-year APM stats? Are Aaron's 2-year APM stats on basketballvalue.com all there is? If that's the case, I really will try to carve out the time to work on this . . .
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PostPosted: Sat Jul 17, 2010 5:28 pm Post subject: Reply with quote
Ilardi wrote:
DSMok1 wrote:

Also--would it be possible to get from you a 4 year, regular season only APM, though 09-10? Then I could use the advanced stats collected by Hoopdata in that time to run a more comprehensive SPM.


I haven't run it yet, but maybe your request will be just the catalyst I need. Is it really the case that no one else out there has put out any publicly available multi-year APM stats? Are Aaron's 2-year APM stats on basketballvalue.com all there is? If that's the case, I really will try to carve out the time to work on this . . .


I don't know of any other APM's out there, now that the RAPM was taken down. The one I could use would be an "average" APM over the last 4 years.
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PostPosted: Mon Jul 19, 2010 9:53 am Post subject: Reply with quote
Neil Paine wrote:
Yeah, SRS is actually just SOS-adjusted point differential per game, which means it's not tempo-independent (we do it that way because we only have game possessions going back to 1986-87). If we had historical SOS-adjusted efficiency differential, that would definitely be the thing to sum to, but since we don't, I'm probably going to just sum to efficiency differential (which is what APM does anyway).

In case I didn't say so, like this new regression a lot! The most glaring problem with the old regression was that it drastically overvalued assists (and therefore PGs -- I found that the average PG was +1 or so while every other position was near zero), but it looks like you fixed this by tying AST% to the scoring term instead of having it stand alone. I would imagine this retrodicts better than the old regression as a result.

...

One troubling result at a first glance is that Dennis Rodman's 1995 is +10.91, one of the greatest seasons of all time... Maybe the rebounding term needs to be re-evaluated?
(Posted from an email)

It looks like the rebounding term will need some more work. The cubic works for just about everyone, except Rodman. He breaks the regression. The 30% TRB% is way out into the nonlinear term, and is worth like 9 points more than D-Howard's 22% TRB%.

Here are a few possibilities:



The cubic is the best fit, but only by a hair. The power + Sq is very close in terms of fit, and would probably be my pick to use. The pure power curve can't capture the desired up-turn at higher TRB% rates, but in terms of fit is still very close to power+Sq (most of the difference is out where there aren't any observations). The linear is here for reference (incidentally, TRB% by itself is a BETTER fit than ORB% and DRB% split out).
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PostPosted: Mon Jul 19, 2010 10:19 am Post subject: Reply with quote
DSMok1 wrote:
...
I'm hoping this doesn't undervalue great centers...


This is reminiscent of a discussion starting with Nazr Mohammed (this year), that many of his rates resembled prime Moses, Gilmore, and others. Low versatility index the likely culprit.

It was asked then whether those known greats were also undervalued by the (then most current) SPM method.

If versatile less-than-great centers (Divac, Daugherty) seem to be better than Moses or Artis, then maybe it needs to be fixed?

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PostPosted: Wed Dec 08, 2010 12:57 pm Post subject: Reply with quote
Ah, okay. Thanks for making the data readily available for the public! Much appreciated.
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PostPosted: Wed Dec 15, 2010 11:31 am Post subject: Reply with quote
I'm preparing to evaluate salaries and contracts, so I'm working on long-term projections based upon the latest updated true-talent level.

Obviously not all players will age the same; some of the young guns will probably jump to transcendant status like CP3, Lebron, and D-Wade start out. We just don't know who, yet!

Here's the pretty picture:


Those are the top 25 projected players in the 2015-2016 season.

Note some of the rookies from this year moving up! Also note OKC's roster--3 players present.
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PostPosted: Mon Dec 20, 2010 7:32 pm Post subject: Reply with quote
Updated Spreadsheet: https://docs.google.com/leaf?id=0Bx1NfC ... MzRl&hl=en
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PostPosted: Mon Dec 20, 2010 9:13 pm Post subject: Reply with quote
DSMok1 wrote:

Obviously not all players will age the same; some of the young guns will probably jump to transcendant status like CP3, Lebron, and D-Wade start out. We just don't know who, yet!



I hope CP3 is around in 5 years, but his knees may be mush by then.
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PostPosted: Mon Dec 20, 2010 9:22 pm Post subject: Reply with quote
EvanZ wrote:
DSMok1 wrote:

Obviously not all players will age the same; some of the young guns will probably jump to transcendant status like CP3, Lebron, and D-Wade start out. We just don't know who, yet!



I hope CP3 is around in 5 years, but his knees may be mush by then.


Yeah. I'd expect outliers like him to age more rapidly.
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PostPosted: Thu Jul 22, 2010 11:12 am Post subject: Reply with quote
DSMok1 wrote:
Here's the regression, with the TRB power term and a linear term only. Honestly, the fit is similar enough that the TRB^2 additional term is probably purely overfitting. (You were right, Rhuidean.)

Here is that regression:
Code:
TRB% -0.114650868
TRBPower 6.762898760
TRBExponent 0.284850151

STL% 1.484282673
BLK% 0.333514467
MPG 0.103521312

TO% Coeff 0.628638746
PPP Threshold 1.634054153
PPP USG Scale 0.013865918
PPP AST Scale 0.009744137
Scoring 0.579187325
USG Const 3.910166612

Intercept -12.466987594



I discovered a flaw in my calculations; I had a slight regression-to-replacement applied to the APM. Removing it doesn't change the SPM terms much, but slightly increases the overall spread. Corrected SPM:
Code:
TRB% -0.11262729
TRBPower 7.21103324
TRBExponent 0.27533883

STL% 1.52798518
BLK% 0.34027348
MPG 0.10394047

TO% Coeff 0.63662985
PPP Threshold 1.64666575
PPP USG Scale 0.01397684
PPP AST Scale 0.00970050
Scoring 0.58831902
USG Const 4.28737016

Intercept -12.78185481

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PostPosted: Thu Jul 22, 2010 12:48 pm Post subject: Reply with quote
I just went through and estimated OSPM and DSPM from the same data, except that the 1 year estimates did not include OAPM and DAPM split up.

Here is Offensive SPM:
Code:
TRB% -0.09696127
TRBPower 12.81133914
TRBExponent 0.11844250

STL% 0.27096567
BLK% -0.08060675
MPG 0.05489518

TO% 0.53648983
PPP Thresh 1.25957931
PPP USG Scale 0.00884937
PPP AST Scale 0.00845557
Scoring 0.59905610
USG Coeff 8.78684193

Intercept -16.03676076


And Defensive SPM:
Code:
TRB% -0.07702830
TRBPower 15.09091745
TRBExponent -0.06311682

STL% -1.23381652
BLK% -0.41721519
MPG -0.04970989

TO% -0.05031619
PPP Thresh -4.96111508
PPP USG Scale -0.05976497
PPP AST Scale 0.00216782
Scoring 0.06565780
USG Coeff 29.80487400

Intercept -23.96225822


1) On the Defensive SPM, NEGATIVE IS GOOD.

2) I'm sure some of these variables are insignificant.

3) Splitting into offensive and defensive rebounding could be beneficial for these, I suppose.

4) These do not sum perfectly to the SPM regression above. Usually within .05, however.

5) The Defensive SPM can do some weird things with low-minute players, it seems (with the negative (=good) intercept).
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PostPosted: Fri Jul 23, 2010 10:37 am Post subject: Reply with quote
DSMok1:
Could you tell us the marginal value of one unit of each main boxscore stat under your current SPM?

And a question: have you ever looked to see if two separate models, one for C/F and one for Guards, improves predictive power at all? I assume it doesn't or someone would have done it by now, but intuitively it seems like coefficients might change.
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PostPosted: Fri Jul 23, 2010 10:46 am Post subject: Reply with quote
Guy wrote:
DSMok1:
Could you tell us the marginal value of one unit of each main boxscore stat under your current SPM?

And a question: have you ever looked to see if two separate models, one for C/F and one for Guards, improves predictive power at all? I assume it doesn't or someone would have done it by now, but intuitively it seems like coefficients might change.


The marginal value of one unit of each boxscore stat depends. I'm using advanced stats (obviously) to calculate, so even the linear terms vary depending on, for example, how many 2's were taken by the opponent (for the block term).

For rebounds, it is a power curve, so not equal. Somewhere in the area of 0.23 points per each % of TRB added, but obviously varying.

For the scoring term, it's a 4 dimensional surface, so rather hard to plot. Maybe I can put up a spreadsheet calculator to experiment with.

As for splitting up... well, I haven't worked with one with this regression. The problem is that positions are both continuous and ambiguous. I can tell a PG away from a Center, but not always a PG away from a SF. (What was Lebron, anyway?). Because of that fact, I generally feel it's not useful.

Besides, the results from the current regression seem to be doing quite well. The offensive side mimics APM well; the defensive side is limited by the terms to input.
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PostPosted: Fri Jul 23, 2010 11:31 am Post subject: Reply with quote
Thanks. So if I'm following, one rebound adds something like .25-.30 points. Would be interesting to know implied value of a marginal assist as well (assuming average team/opponent).
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PostPosted: Fri Jul 23, 2010 11:45 am Post subject: Reply with quote
Guy wrote:
Thanks. So if I'm following, one rebound adds something like .25-.30 points. Would be interesting to know implied value of a marginal assist as well (assuming average team/opponent).


Assists are totally wrapped up in the scoring term. I just picked a random player (JJ Reddick, in this case) and added another % to his AST%. His SPM went up 0.13.

But that will vary mightily based on USG%, because the assist term is multiplied by usage.
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PostPosted: Fri Jul 23, 2010 1:06 pm Post subject: Reply with quote
For interests' sake: an example of the this new SPM in action:

NBA Finals, 09-10:
Code:
Player SPM %Min Contrib VORP NBA SPM NBA VORP
Kobe Bryant 5.91 85.8% 5.06 7.64 7.51 9.01
Pau Gasol 4.82 87.3% 4.21 6.83 6.42 8.22
Ron Artest -1.43 74.7% -1.07 1.17 0.17 2.37
Lamar Odom -1.30 57.2% -0.74 0.97 0.30 1.89
Derek Fisher -1.99 63.7% -1.27 0.64 -0.39 1.66
Sasha Vujacic 0.85 15.5% 0.13 0.60 2.45 0.84
Andrew Bynum -2.19 52.1% -1.14 0.42 -0.59 1.25
DJ Mbenga -13.14 0.9% -0.12 -0.09 -11.54 -0.08
Josh Powell -12.23 2.4% -0.29 -0.22 -10.63 -0.18
Shannon Brown -4.68 25.0% -1.17 -0.42 -3.08 -0.02
Jordan Farmar -4.88 26.2% -1.28 -0.49 -3.28 -0.07
Luke Walton -9.49 9.2% -0.88 -0.60 -7.89 -0.45

Player SPM %Min Contrib VORP NBA SPM NBA VORP
Kevin Garnett 4.70 66.1% 3.11 5.09 6.30 6.15
Rajon Rondo 2.87 81.0% 2.32 4.75 4.47 6.05
Paul Pierce -0.13 82.8% -0.11 2.37 1.47 3.70
Glen Davis -0.15 42.9% -0.06 1.22 1.45 1.91
Rasheed Wallace -1.02 42.9% -0.44 0.85 0.58 1.54
Nate Robinson -0.37 21.1% -0.08 0.56 1.23 0.89
Kendrick Perkins -2.02 42.0% -0.85 0.41 -0.42 1.08
Marquis Daniels 1.04 1.2% 0.01 0.05 2.64 0.07
Tony Allen -3.03 30.7% -0.93 -0.01 -1.43 0.48
Brian Scalabrine -16.39 0.3% -0.05 -0.04 -14.79 -0.04
Michael Finley -22.93 1.5% -0.34 -0.30 -21.33 -0.27
Ray Allen -3.50 82.2% -2.87 -0.41 -1.90 0.91
Shelden Williams -21.50 5.4% -1.15 -0.99 -19.90 -0.91


What I'm showing is the SPM (already team-adjusted to match up to the efficiency differential, but this adjustment was less than 0.1 for each team), the minutes played, the contribution (SPM*%Min), the VORP (SPM+3)*%Min, and SPM and VORP adjusted for the level of competition (I assumed that these teams were averaging a +8 efficiency differential level, and added that to the SPM).

This new regression does recognize Kobe as superior to Pau, but only by a little. Compare with my old beta regression: viewtopic.php?p=31839#31839. It's a big difference!
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PostPosted: Mon Jul 26, 2010 1:12 pm Post subject: Reply with quote
I noted a few posts above that the offensive and defensive SPM had some unnecessary variables included. For instance though shooting is statistically significant for defense (a good shooter = bad defender) it should not be included in the regression. We can't just ASSUME that a good shooter will be a bad defender. It's just that a bad shooter that's playing in the NBA must be a good defender, or else he wouldn't be here!

So, throwing out tangential variables, here are the offensive and defensive regressions for OSPM and DSPM:

Here is Offensive SPM:
Code:
TRB% -0.20610998
TRBPower 8.42678761
TRBExponent 0.20247387

MPG 0.08242452

TO% 0.63261410
PPP Thresh 1.35785021
PPP USG Scale 0.00926961
PPP AST Scale 0.00957339
Scoring 0.56025531
USG Coeff 7.01988471

Intercept -10.92774435


And Defensive SPM (with negative being good):
Code:
TRB% -0.14025543
TRBPower -1.64008765
TRBExponent 0.19101623

STL% -1.45142242
BLK% -0.41795713
MPG 0.00344333

Intercept 6.52648729


How well do these fit the data? Well, I'll report R-squared results here, just to give an idea. I didn't weight all data points evenly (based on the error in the APM) in the regression, so take these numbers with a lump of salt.

Overall SPM: 0.28
Offensive SPM: 0.56
Defensive SPM: 0.33
Sum of OSPM and DSPM (comparing to overall APM): 0.27

These new offensive and defensive SPM's will not sum to the overall SPM. The average difference between the Sum and SPM is around 0.3 to 0.4, so not too far off, but not great either.

I would recommend using these offensive and defensive SPM's over those above that included insignificant/inappropriate variables.

Also, remember to sum/adjust each of these to force the team totals to equal the team's efficiency above or below NBA average. (It guess that's what we should sum to--right?)

EDIT:

Probably better to use ORB and DRB instead of TRB when doing the specific regressions for OSPM and DSPM:

Code:
ORB% -0.10129651
ORBPower 5.16775677
ORBExponent 0.15790017

MPG 0.08366916

TO% 0.65655052
PPP Thresh 1.35219734
PPP USG Scale 0.00887959
PPP AST Scale 0.00971672
Scoring 0.56548199
USG Coeff 7.46146945

Intercept -5.66757625


And Defensive SPM (with negative being good):
Code:
DRB% -0.04258455
DRBPower -5.48349226
DRBExponent 0.16254300

STL% -1.42555701
BLK% -0.45616939
MPG 0.01151452

Intercept 11.43405907


The TRB forms behaved oddly for high rebounding percentages on offense. Use these lower forms!
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PostPosted: Fri Aug 06, 2010 12:05 pm Post subject: Reply with quote
I've added a nonlinear assist term experimentally; it seems to help considerably, but reduces the accuracy at the extremes (i.e. 0% AST).

Here is the NEW SPREADSHEET with lots of additional columns and calculations.

Including True Value II, my regressed best estimate of the player's value.

In actual dollars!
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PostPosted: Fri Aug 06, 2010 2:41 pm Post subject: Reply with quote
How much weight does TM DRtg get in DSPM? Would it make sense to use only the DRtg when the player is on the court?
It seems that good defenders on bad teams will get hurt by this, notably Amir Johnson. When he's in, the Raptors were close to a league average defense (107.92). It seems kind of unfair to adjust him to his team's awful rating, when most of the damage was done while he was on the bench.
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PostPosted: Sat Aug 07, 2010 8:47 am Post subject: Reply with quote
DSMok1 wrote:
I've added a nonlinear assist term experimentally; it seems to help considerably, but reduces the accuracy at the extremes (i.e. 0% AST).

Here is the NEW SPREADSHEET with lots of additional columns and calculations.

Including True Value II, my regressed best estimate of the player's value.

In actual dollars!


Awesome, thanks. Intriguing predictive outlook too.
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PostPosted: Wed Aug 11, 2010 11:56 am Post subject: Reply with quote
I'm sure this is blatantly obvious and I'm just having a senior moment, but what is the Rk column? (column B)
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PostPosted: Wed Aug 11, 2010 2:04 pm Post subject: Reply with quote
battaile wrote:
I'm sure this is blatantly obvious and I'm just having a senior moment, but what is the Rk column? (column B)


Just an artifact of the data from Basketball Reference. I should have deleted it... It was the "rank" of players on each team by win shares.
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PostPosted: Thu Aug 12, 2010 11:41 am Post subject: Reply with quote
DSMok1 wrote:
battaile wrote:
I'm sure this is blatantly obvious and I'm just having a senior moment, but what is the Rk column? (column B)


Just an artifact of the data from Basketball Reference. I should have deleted it... It was the "rank" of players on each team by win shares.


Ah cool, thanks!

Is there a post somewhere that explains the various columns? I'm pretty fascinated by this spreadsheet but struggling to understand some of the relationships. (like looking at Ariza's mostly pedestrian advanced stat numbers through column W and figuring out what it is about him that gives him a true value over 9m, etc)
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PostPosted: Thu Oct 07, 2010 12:15 pm Post subject: Reply with quote
A couple of spreadsheets:
All players since 1978, full Advanced SPM numbers
and
An example of 1 year's full calculations, including a macro to update to other years or within this coming year.
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Last edited by Crow on Thu May 12, 2011 6:49 am, edited 2 times in total.

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PostPosted: Thu Oct 07, 2010 1:07 pm Post subject: Reply with quote
DSMok1 wrote:
A couple of spreadsheets:
All players since 1978, full Advanced SPM numbers
and
An example of 1 year's full calculations, including a macro to update to other years or within this coming year.


Awesome. Awesome. Awesome.

Thank you so much for taking the time to compile this data.
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PostPosted: Thu Oct 07, 2010 3:49 pm Post subject: Reply with quote
erivera7 wrote:

Awesome. Awesome. Awesome.

Thank you so much for taking the time to compile this data.


My objective is a full Advanced SPM projection system. Not sure if I'll get that done before the season. I'll probably get some rough numbers out at the very least.

A quick, interesting chart: the best 10 seasons of the top 20 players since 1977 (Seasons are Advanced SPM VORP, careers were measured by total VORP.)




Recognize that from sabermetrics, anybody?
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PostPosted: Thu Oct 07, 2010 4:20 pm Post subject: Reply with quote
This is like Christmas. Thank you.
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PostPosted: Thu Oct 07, 2010 4:32 pm Post subject: Reply with quote
Biggest surprise to me was how high Karl Malone's peak seasons were.

The relative flatness of his VORP curve was not surprising, he was both Mr. Consistency and Mr. Longevity, both. So when we look at his 8th - 10th best seasons, they're second only to Mr. Airness.

That he was that high was slightly surprising, the big surprise to me was that his peak season was behind only Jordan, Robinson, and Stockton (and basically tied with Garnett, Shaq, and I think Kobe (the graph gets crowded there). I hadn't thought of Malone as being quite THAT good.

Or to put it another way, his entire curve is higher than Tim Duncan's; if I'm building an all-time team of all-time players, my instinct is to take Duncan over Malone. Probably Kevin Garnett too (though he's a different style of player). But the graph shows Garnett essentially tied with Malone during their top 3 seasons, with Garnett falling behind in seasons 4-10.

I don't know if I buy John Stockton having the 3rd best peak season of all of these 20 players.
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PostPosted: Thu Oct 07, 2010 8:03 pm Post subject: Reply with quote
Out of curiosity, how does LeBron James stack up with that top 10?

As an aside, I'm surprised Allen Iverson appears on the list.

Don't have a particular reason for that reaction, other than the fact he was almost always a high usage/low efficiency player in his prime.
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PostPosted: Thu Oct 07, 2010 10:15 pm Post subject: Reply with quote
erivera7 wrote:
Out of curiosity, how does LeBron James stack up with that top 10?

As an aside, I'm surprised Allen Iverson appears on the list.

Don't have a particular reason for that reaction, other than the fact he was almost always a high usage/low efficiency player in his prime.


James is in the top 20 of the era, but didn't have 10 season so I didn't include him. His top 6 seasons are second only to MJ.

AI is an outlier--it's hard to get a handle on his worth. I don't know if the regression captures the value at that extremity properly.

Also, mtamada, hasn't MikeG shown that Stockton's assists were significantly overstated? That would make a significant change in his value.

Also--I thought that it was well known that Malone was the best PF of all time? The Jazz were so good for so long for some reason--remember, these teams all sum to their efficiency differential. Stockton and Malone drove those teams. You can sort the listing by team and year and look at the other players on those teams and see what the team efficiency differential was and what team adjustment was applied.
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PostPosted: Thu Oct 07, 2010 11:49 pm Post subject: Reply with quote
Unless something has changed recently, Advanced SPM does not directly and separately address the shot defense of players and so a lot of people might still select Duncan or Garnett. Or rate Iverson lower after considering defense and perhaps impact on teammate's offensive efficiency beyond assists, things that Adjusted +/- encompasses.

Some other models make a simple everybody on the team is equal patch on shot defense, but Adjusted +/- is the only one that fully considers impact on defense and teammate's offensive efficiency, beyond assists and offensive rebounds and, in the case of PER, usage (though PER uses one simple function for everybody rather than attempting to look at individual cases).

Rebounds, blocks, steals and fouls may get assigned the additional value of good shot defense in Advanced SPM for lack of anywhere else for it to go. If your shot defense quality (1 on 1 and help / team shot defense) varies significantly from your defensive performance on the counted defensive stats, your overall rating may be too high or too low for as a result. And if players have different performance ratios on the uncounted shot defense relative to the counted defensive stats, the comparison will be affected as well.

The simplifying assumptions that the shot defense for all teammates or even all players is the same, or that it is impossible to make any reasonable measurements or estimates of shot defense are options; but they become caveats to the ratings if you make either.

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PostPosted: Fri Oct 08, 2010 12:04 pm Post subject: Reply with quote
Crow wrote:
Unless something has changed recently, Advanced SPM does not directly and separately address the shot defense of players and so a lot of people might still select Duncan or Garnett. Or rate Iverson lower after considering defense and perhaps impact on teammate's offensive efficiency beyond assists, things that Adjusted +/- encompasses.

Some other models make a simple everybody on the team is equal patch on shot defense, but Adjusted +/- is the only one that fully considers impact on teammate's offensive efficiency, beyond assists and offensive rebounds and, in the case of PER, usage (though PER uses one simple function for everybody rather than attempting to look at individual cases).

Rebounds, blocks, steals and fouls may get assigned the additional value of good shot defense in Advanced SPM for lack of anywhere else for it to go. If your shot defense quality (1 on 1 and help / team shot defense) varies significantly from your defensive performance on the counted defensive stats, your overall rating may be too high or too low for as a result. And if players have different performance ratios on the uncounted shot defense relative to the counted defensive stats, the comparison will be affected as well.

The simplifying assumptions that the shot defense for all teammates or even all players is the same, or that it is impossible to make any reasonable measurements or estimates of shot defense are options; but they become caveats to the ratings if you make either.


Right, Crow. However, I question how much individual defense can actually vary, compared to offense. The scatter in RAPM and 6-Year APM is much greater on offense than defense, indicating there is a much wider talent spread on offense than on defense.
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PostPosted: Fri Oct 08, 2010 12:44 pm Post subject: Reply with quote
There's a lot to consider here. 'shooting defense' alone needs to be unpacked a little bit so we're all on the same page. Do we include some sort of defensive usage and consider volume? I do not have a synergy account, but from what I understand of the cheap one there's nothing there that's a satisfying proxy for field scoring prevented.

We don't have any tools for poking at that tangle besides adj. +/-. It might show us the blind spot but in most cases that is not enough. The decision between Duncan, Malone and Garnett probably comes down to scoring defense. For perimeter players who aren't involved in defensive rebounding as much, it rates as even more important.

Assuming that adjusted +/- will identify good or bad defenders when you compare it to other metrics is useful but won't be conclusive. For the purposes of SPM or linears it hardly seems better than assigning team defensive stats to individuals by minutes played. A weighty, clunky proxy will just interfere with what you might have learned.

I think it's better to use what we have (even at the risk of inflating the importance of stl%, blk% and dreb%) and basically keep in mind that scoring defense isn't going to show up in box score metrics.
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PostPosted: Fri Oct 08, 2010 12:55 pm Post subject: Reply with quote
The thing is: we don't have APM for Karl Malone. All we have are the stats I have here. The primary point of this ASPM regression was to use the best data we have for the last 30 years to work up a good understanding of the players, and to develop a projection system based on that length of history.
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PostPosted: Fri Oct 08, 2010 1:15 pm Post subject: Reply with quote
DSMok1 wrote:
The thing is: we don't have APM for Karl Malone. All we have are the stats I have here. The primary point of this ASPM regression was to use the best data we have for the last 30 years to work up a good understanding of the players, and to develop a projection system based on that length of history.


I think you did a great job, I'm enjoying looking through your downloadable content. Thanks for making it public.
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PostPosted: Fri Oct 08, 2010 1:44 pm Post subject: Reply with quote
For a long historical survey ASPM is a good metric given that play by play based counterpart defensive stats and Adjusted +/- are only readily available for 6-8 years. Just wanted to mention the caveats again.


The number of players lower than +3 on one multi-season version of RAPM or higher than +3 on defense is about 40% less than on offense and the total range from max to min is about 30% less. But it is still half the game.

Shot defense is about half of that half. A fairly significant amount of value that one way or another I'd try to assess at least for the recent seasons and from here on. Cobbled unto the rating or added manually after seeing the rating. The advantage of cobbling it on to everyone's listed rating is that you don't forget and you treat everyone the same.

But you have to select a methodology. 100% counterpart match-up shot defense stats is not fully satisfactory as a substitute to wholly using team stats. Averaging the 2 is one way rough way to do it. Converting the match-up shot defense stats into points allowed compared to league average eFG% allowed and usage faced.

Using the shot defense factor of Adjusted +/- to cover this missing piece is attractive to me conceptually to avoid the above steps, but the public view of that data was single-shot so far. I can cobble that data onto ASPM or another metric case by case at least for last season and maybe next.



Having an old version of Excel I can't see the latest files but I can accept that as my loss for the time being. Unless others have a similar limitation and another version is not too much trouble.

The graphs are always interesting. Thanks.
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PostPosted: Fri Oct 08, 2010 4:38 pm Post subject: Reply with quote
Thanks, Rob.

Crow, anytime anyone goes subjective I'm wary. You can't get shot defense out of APM; in fact you can't get it out of any of the numbers in my opinion. There's too much noise in APM to disentangle it.

I wanted to mention: if you have CHARGES TAKEN, then you can add that directly into the regression. Charges taken should be taken as a % of total defensive possessions, and I have found them to be directly equal to a steal. In other words: if a player has a 2.1 STL% and 40 steals, and has 20 charges taken, his updated STL/CHG% is 3.05%. And that directly works in the spreadsheet. That better distributes defensive value.
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PostPosted: Fri Oct 08, 2010 7:39 pm Post subject: Reply with quote
DSMok1 wrote:


Crow, anytime anyone goes subjective I'm wary. You can't get shot defense out of APM; in fact you can't get it out of any of the numbers in my opinion. There's too much noise in APM to disentangle it.


I found Joe Sill's factor analysis including impact on eFG% allowed useful. The errors were pretty low in the multi-season version and not worse than the roll=up RAPM. That was an objective approach. It is subjective how much to rely on it or to reject it.

ASPM is based on regression for stats across the league as a whole and will have error too (in terms of point differential / win impact) when applied to individual players.

No metric is perfect, completely simple and obvious. Recognize limitations, add other forms of evaluation, compare and then make judgments. Rinse, repeat... or do something different if you think it will be better.
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PostPosted: Fri Oct 08, 2010 8:38 pm Post subject: Reply with quote
I saw Ryan, Eddy, and haralabob talking on twitter about this: why were Chris Paul, Lebron, and Wade equal to or better than Jordan's best year in this metric?

A couple of factors, I think: first, the metric was regressed on a time period when by APM the recent 3 were near or at the top. Jordan wasn't there with his (likely even higher) APM. So the metric probably doesn't capture what he did as well.

That said, compare their best seasons: http://www.basketball-reference.com/pla ... i?id=GrceH

The advanced stats of those 3 compare quite favorably with MJ! When you look at those 3, MJ, and Magic, you have various players at the top in various categories. How their best seasons are ordered depends on which metric you look at. ORtg has Magic at the top (it doesn't penalize for turnovers as much). O Win Shares has Jordan at the top. PER has Lebron with the best season. I have CP3--I value assists quite a lot, like ORtg, but I penalize for turnovers more than ORtg. This wasn't intentional--it's just how regressing these advanced stats onto the best APM's available ended up.
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PostPosted: Fri Oct 08, 2010 9:14 pm Post subject: Reply with quote
Jordan has 8 of 9 of the lowest assist ratios on the linked list, only surpassing McGrady.

How much of an impact, all other things equal, do the 10, 20, 30 percentage point differences in assist ratio have on Offensive Rating?

If the assist ratio set equal to compare on the rest of the OR formula would he blow them away or would it still be tight or in-between?

You can say they all had the same opportunity to do well on assist ratio or you could say Jordan's role was different.

Jordan has 4 of the top 5 on PER for the group. 5 of the top 6 on Win Shares and 8 of top 12. 3 of the top 4 on WS/48. 7 of the top 9 on Defensive Win Shares. Even 5 of 10 of Offensive Rating, his weakest metric on the page.

Only 4 others on that particular list. None more than 3 times, so far. The list will change as 2 of the actives finish their careers and perhaps others meet the specified criteria. No max on the rebounding % criteria would let 5 others in- O"Neal, Nowitski, D Robinson and Karl Malone with 1 each and Barkley with 3 and a tie with Magic for 2nd most.
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PostPosted: Sat Oct 09, 2010 8:30 am Post subject: Reply with quote
Crow wrote:

I found Joe Sill's factor analysis including impact on eFG% allowed useful. The errors were pretty low in the multi-season version and not worse than the roll=up RAPM.


Crow, do you have a link for Sill's factor analysis? I didn't realize he had conducted one, but it's something I had been planning for a while . . .
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PostPosted: Sat Oct 09, 2010 9:00 am Post subject: Reply with quote
Ilardi wrote:
Crow wrote:

I found Joe Sill's factor analysis including impact on eFG% allowed useful. The errors were pretty low in the multi-season version and not worse than the roll=up RAPM.


Crow, do you have a link for Sill's factor analysis? I didn't realize he had conducted one, but it's something I had been planning for a while . . .


It was on his site, but I think all of his site is gone.
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PostPosted: Sat Oct 09, 2010 5:01 pm Post subject: Reply with quote
Do you recall the major variables in the factor analysis?
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PostPosted: Sat Oct 09, 2010 5:24 pm Post subject: Reply with quote
By "factor analysis" I just meant he broke Adjusted +/- into the standard 4 factors of Offense and Defense.

I was surprised to never hear anyone else publicly use and cite the data. When I did cite it, folks often ignored or rejected the data entirely. Not sure if they checked the standard errors or tried to see what it "showed". I found it quite useful even with the standard concerns about imprecision. For general guidance (i.e. he looks good / average / below average of this Factor or strongly so). But in case of the occasional very surprising result I'd ask why it turned out that way and try to find a basis. Sometimes it might be a heavily affected by error outlier but it is a sign to try to look into it more.
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PostPosted: Sun Oct 10, 2010 4:17 pm Post subject: Reply with quote
Crow wrote:

Jordan has 4 of the top 5 on PER for the group. 5 of the top 6 on Win Shares and 8 of top 12. 3 of the top 4 on WS/48. 7 of the top 9 on Defensive Win Shares. Even 5 of 10 of Offensive Rating, his weakest metric on the page.


I have Jordan with 4 of the top 10 years in ASPM, Lebron with 2, CP3 with 2, Wade with 1, and David Robinson with 1.

Compare Jordan's best (88 or 89) with Lebron's best (09 or 10). Lebron has far higher AST%, similar USG, similar TS%, slightly higher TO%, lower STL%, higher BLK%, and slightly higher RB%. It's quite easy, from the numbers, to argue Lebron as Jordan's equal.

In the regular season, of course.
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PostPosted: Sun Oct 10, 2010 5:37 pm Post subject: Reply with quote
James' last 2 seasons were 2 of his 3 seasons of 103 or better on Defensive rating out of 7 tries. No titles yet.

Jordan was 103 or better on Defensive rating on 10 of 15 tries. 6 titles.

Defensive Rating is a mix of personal defensive accomplishment and player on team accomplishment.

Be like the recent James and what Jordan was for 9 of 10 years beginning with his 4th season (Pippen and Grant arrived then, followed by Jackson the next season) 'til he left Chicago and James will have a good chance to win some titles and be closer to Jordan in overall value and titles.
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PostPosted: Sun Oct 10, 2010 8:23 pm Post subject: Reply with quote
Crow wrote:

Defensive Rating is a mix of personal defensive accomplishment and player on team accomplishment.


That's what the defensive component of ASPM is, also. Pretty similar, I think.
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PostPosted: Sun Oct 10, 2010 9:01 pm Post subject: Reply with quote
revised-

What part of ASPM is accounting for player on team defensive accomplishment? It is not accounting for shot defense which is what I referring to with respect to Defensive Rating.

Do you still prefer to based overall ASPM on total rebounding%? I might personally prefer ASPM to be equal to OASPM + DASPM so that offensive and defensive rebounding got weighted separately.

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PostPosted: Sun Oct 10, 2010 9:15 pm Post subject: Reply with quote
Crow wrote:
What part of ASPM is accounting for player on team defensive accomplishment? It is not accounting for shot defense which is what I referring to with respect to Defensive Rating.

Do you still prefer to based overall ASPM on total rebounding%? I might personally prefer ASPM to be =OASPM + DASPM so that offensive and defensive rebounding got weighted separately. But the extremely low weight for defensive rebounding (if I recall correctly) makes that less appealing; so perhaps your approach works out alright.


Both independent offensive and defensive ASPM and the cumulative ASPM are on the spreadsheets; you can look at the weights yourself. The cumulative ASPM with TRB% used correlated slightly better than the sum of the component ASPM's.
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PostPosted: Sun Oct 10, 2010 9:22 pm Post subject: Reply with quote
Alright thanks for the rationale on the latter point. That the overall ASPM and the splits don't exactly match-up is something I'll keep in mind along with other things.
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PostPosted: Mon Oct 11, 2010 1:38 pm Post subject: Reply with quote
Steve, have you seen this old factor analysis thread?

viewtopic.php?t=444

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PostPosted: Thu Oct 14, 2010 7:54 pm Post subject: Reply with quote
DSMok1,

Have you run year to year+1 correlations for ASPM?

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PostPosted: Sun Oct 17, 2010 9:32 pm Post subject: Reply with quote
Some new work on the draft: this is for the rookie year:



Since bad draftees don't get to play, I assumed a normal distribution of the players and estimated (from the players that actually played) what the median player was and what the standard deviation of the distribution was. It's more helpful for the second round draft picks.

Interestingly, I found that in the rookie year, for a given pick the younger players generally perform better. Perhaps because their aging curve is steeper and they improve more from college to their first pro year?
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PostPosted: Sat Nov 13, 2010 11:07 am Post subject: Reply with quote
I'm working up how to apply Advanced SPM to a single game. Because the stats in a single game are so granular, the best way to apply the regression is to run Advanced SPM for the team with and without the game, and infer the contributions from the game from the difference between the results with and without the game.

For example: last night, the Suns played the Kings.

I ran the full NBA regression before last night's games and after last night's games. I generated the ASPM for each player on the teams for last night by back calculating the ASPM required last night to move the season numbers by as much as they moved.

Here are the results:
Code:
Team Player MP Prev SPM Prev SPM Now Change Gm SPM Gm MP Gm Contrib Gm VORP
PHO Steve Nash 234 2.34 5.61 3.27 27.5 35 20.0 22.6
PHO Hakim Warrick 187 0.17 1.25 1.08 10.0 23 4.8 6.5
PHO Goran Dragic 112 -0.80 0.80 1.59 14.5 13 3.9 4.9
PHO Josh Childress 119 -2.46 -1.60 0.86 2.5 25 1.3 3.1
PHO Robin Lopez 136 -6.19 -5.63 0.56 -1.7 19 -0.7 0.7
PHO Grant Hill 198 0.02 -0.24 -0.26 -2.7 21 -1.2 0.3
PHO Garret Siler 17 -14.28 -14.44 -0.16 0.0 0 0.0 0.0
PHO Channing Frye 177 -2.47 -2.72 -0.26 -4.3 29 -2.6 -0.5
PHO Hedo Turkoglu 181 0.78 0.12 -0.66 -4.6 25 -2.4 -0.6
PHO Jason Richardson 234 3.18 2.21 -0.97 -4.5 34 -3.2 -0.7
PHO Jared Dudley 136 -0.12 -2.03 -1.91 -18.2 16 -6.1 -4.9

Team Player MP Prev SPM Prev SPM Now Change Gm SPM Gm MP Gm Contrib Gm VORP
SAC Tyreke Evans 209 2.13 2.49 0.36 4.3 42 3.7 6.8
SAC Carl Landry 201 -4.83 -3.72 1.11 2.6 35 1.9 4.5
SAC DeMarcus Cousins 150 -0.78 -0.63 0.15 0.5 21 0.2 1.7
SAC Beno Udrih 253 0.57 0.29 -0.28 -1.7 36 -1.3 1.4
SAC Omri Casspi 191 -1.88 -1.86 0.02 -1.7 35 -1.3 1.3
SAC Francisco Garcia 187 4.20 3.54 -0.66 -3.0 19 -1.2 0.2
SAC Hassan Whiteside 2 -11.96 -12.02 -0.06 0.0 0 0.0 0.0
SAC Jason Thompson 108 -3.67 -3.75 -0.09 0.0 0 0.0 0.0
SAC Donte Greene 34 -5.24 -5.30 -0.07 0.0 0 0.0 0.0
SAC Eugene Jeter 4 -27.19 -27.31 -0.11 0.0 0 0.0 0.0
SAC Luther Head 95 -1.21 -1.59 -0.38 -13.5 3 -0.8 -0.6
SAC Samuel Dalembert 142 -1.03 -1.78 -0.74 -6.0 25 -3.1 -1.3
SAC Antoine Wright 5 -23.13 -27.98 -4.84 -30.4 10 -6.3 -5.6
SAC Darnell Jackson 99 -3.24 -5.63 -2.39 -20.4 16 -6.8 -5.6

As can be seen, Steve Nash totally dominated this game, racking up a rating of 27.5 points above NBA average, per 100 possessions. Wow! That's better than most games even by Lebron, CP3, and D-Wade. What did he do that was so amazing?

Code:
Starters MP TS% eFG% ORB% DRB% TRB% AST% STL% BLK% TOV% USG%
Steve Nash 35:26:00 0.709 0.722 3.2 16.3 10.3 81.1 1.6 0 9.2 28.9


Yeah, that was a pretty dominant offensive game!

Incidentally, here were the top and bottom 10 players from last night:
Code:
Tm Player Gm SPM Gm MP Gm Contrib Gm VORP
PHO Steve Nash 27.5 35 20.0 22.6
CHA Gerald Wallace 14.2 40 11.8 14.8
OKC Russell Westbrook 11.9 44 10.9 14.1
MIN Michael Beasley 13.1 40 10.9 13.8
ORL Mickael Pietrus 18.0 30 11.2 13.4
MIN Kevin Love 8.8 41 7.5 10.5
UTA Al Jefferson 10.0 35 7.3 9.8
UTA Deron Williams 8.6 39 6.9 9.8
NYK Wilson Chandler 6.7 42 5.9 8.9
DET Charlie Villanueva 8.3 35 6.1 8.6

Tm Player Gm SPM Gm MP Gm Contrib Gm VORP
WAS Gilbert Arenas -9.5 31 -6.1 -3.9
IND Brandon Rush -10.7 26 -5.8 -3.9
POR Wesley Matthews -19.7 13 -5.3 -4.4
TOR Joey Dorsey -30.3 8 -5.1 -4.5
PHI Jodie Meeks -15.5 18 -5.8 -4.5
MIN Sundiata Gaines -24.3 11 -5.6 -4.8
PHO Jared Dudley -18.2 16 -6.1 -4.9
SAC Antoine Wright -30.4 10 -6.3 -5.6
SAC Darnell Jackson -20.4 16 -6.8 -5.6
WAS Al Thornton -22.2 21 -9.7 -8.2

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PostPosted: Fri Apr 15, 2011 8:10 am 
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Author Message greyberger



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Posted: Sat Nov 13, 2010 12:15 pm Post subject:

Wow kind of takes the air out of Kevin Love's 30-30 game. That Nash and Gerald Wallace had better nights is understandable, especially with the difference between 106 possessions and 87 or 88... but that Micheal Beasley might have been the hero of that game is something that went entirely overlooked in the media. I'm not sure I would have come to that conclusion myself, but there's an case there. Without Beasley's scoring contribution the Wolves would have been 28/72.
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Posted: Sat Nov 13, 2010 12:48 pm Post subject:

greyberger wrote:
Wow kind of takes the air out of Kevin Love's 30-30 game. That Nash and Gerald Wallace had better nights is understandable, especially with the difference between 106 possessions and 87 or 88... but that Micheal Beasley might have been the hero of that game is something that went entirely overlooked in the media. I'm not sure I would have come to that conclusion myself, but there's an case there. Without Beasley's scoring contribution the Wolves would have been 28/72.
That is a little wierd, isn't it! Rebounds are not exceptionally heavily weighted in Advanced SPM. In this case, it's probably deceiving. Code:
Starters MP TS% eFG% ORB% DRB% TRB% AST% STL% BLK% TOV% USG% ORtg DRtg Michael Beasley 40:41 .586 .586 2.4 11.8 7.2 18.8 2.3 1.9 3.2 29.3 127 102 Kevin Love 40:39 .510 .442 28.9 44.9 37.0 19.0 0.0 1.9 6.2 30.8 124 96
They had similar usage, block, and assist numbers. Beasley had considerably higher TS%, STL%, and lower turnovers. Love had the great rebounding. In this case, I'd say that Love probably helped the team more, but it's kind of hard to compare. I think a factor in the numbers being the way they are is that Beasley started with a lower ASPM before this game and it seems to be marginally nonlinear in that it's easier to increase from -3 to 0 than from 0 to 3 for the year, a fact which back-calculating the numbers cannot account for._________________GodismyJudgeOK.com/DStats
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Posted: Thu Nov 18, 2010 8:33 am Post subject:

Another sample of single-game ASPM: Last night's Heat-Suns game: Code:
Player Gm SPM Gm MP Gm Contrib Gm VORP Chris Bosh 22.8 30 14.3 16.5 LeBron James 29.9 23 14.3 16.0 Dwyane Wade 8.6 30 5.4 7.6 Carlos Arroyo 4.5 23 2.1 3.8 Eddie House 1.3 28 0.8 2.8 Jerry Stackhouse 19.3 4 1.6 1.9 Joel Anthony -0.5 16 -0.2 1.0 Udonis Haslem -2.9 27 -1.6 0.4 Jamaal Magloire 0.0 0 0.0 0.0 Juwan Howard -5.4 15 -1.7 -0.6 Zydrunas Ilgauskas -7.6 7 -1.1 -0.6 Mario Chalmers -13.4 5 -1.4 -1.0 James Jones -5.7 30 -3.6 -1.4 Player Gm SPM Gm MP Gm Contrib Gm VORP Channing Frye 3.2 27 1.8 3.8 Hedo Turkoglu 1.4 25 0.8 2.6 Grant Hill 0.1 24 0.0 1.8 Garret Siler 1.5 5 0.2 0.5 Josh Childress -2.2 18 -0.8 0.5 Earl Clark -2.0 13 -0.5 0.4 Robin Lopez 0.0 0 0.0 0.0 Steve Nash -5.3 29 -3.2 -1.1 Earl Barron -15.5 9 -2.9 -2.3 Goran Dragic -9.6 19 -3.8 -2.4 Jared Dudley -11.4 21 -5.0 -3.5 Jason Richardson -10.4 31 -6.7 -4.5 Hakim Warrick -20.1 19 -8.0 -6.6
Despite the raving by the press, Lebron had a significantly better game than Bosh: http://www.basketball-reference.com/box ... 70MIA.html. They had the same VORP for the game, but Lebron did it in 23 minutes!_________________GodismyJudgeOK.com/DStats
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Posted: Sat Nov 20, 2010 7:39 pm Post subject:

Single game for the Thunder/Celtics Yesterday: Code:
Player Gm SPM Gm MP Gm Contrib Gm VORP Shaquille O'Neal 5.9 28 3.4 5.5 Rajon Rondo 3.1 34 2.2 4.7 Kevin Garnett 3.2 30 2.0 4.2 Nate Robinson 2.0 11 0.5 1.3 Ray Allen 0.1 34 0.0 2.5 Delonte West -2.7 17 -1.0 0.3 Marquis Daniels -8.3 12 -2.1 -1.2 Paul Pierce -4.5 36 -3.4 -0.8 Semih Erden -11.9 14 -3.5 -2.5 Glen Davis -7.2 24 -3.6 -1.9 Russell Westbrook 10.7 37 8.2 10.9 Eric Maynor 14.1 13 3.8 4.8 Royal Ivey 5.0 16 1.7 2.8 Nick Collison -1.2 24 -0.6 1.2 D.J. White -3.0 11 -0.7 0.1 Morris Peterson -12.8 5 -1.3 -1.0 James Harden -1.8 37 -1.4 1.3 Serge Ibaka -2.4 36 -1.8 0.8 Thabo Sefolosha -3.0 36 -2.2 0.4 Nenad Krstic -6.9 25 -3.6 -1.8
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Italian Stallion



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Posted: Fri Dec 24, 2010 3:04 pm Post subject:

I'm a huge Knicks fan. I was looking at some adjusted +/- data from another source and noticed that Raymond Felton looks terrible by that metric so far this year. That doesn't jive with box score data, personal observation, the Knicks much improved performance (I realize that Fields has had a huge positive impact) or the fact that IMO he's clearly better than Duhon was last year. Does anyone have an explanation for why he's rating so poorly so far? IMO something is amiss
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Posted: Fri Dec 24, 2010 4:10 pm Post subject:

Well, if you mean just-this-year-so-far, isn't APM over a 30 game sample very noisy? I'm not sure APM is much of an improvement over looking at raw +/- in small samples.
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Posted: Fri Dec 24, 2010 8:21 pm Post subject:

greyberger wrote:
Well, if you mean just-this-year-so-far, isn't APM over a 30 game sample very noisy? I'm not sure APM is much of an improvement over looking at raw +/- in small samples.
It's actually worse than raw +/- at that level, in my opinion. ASPM has Felton as a solid player: +1.75 this year, good for second on the team: Amare Stoudemire 2.56 Raymond Felton 1.89 Wilson Chandler 0.93 Landry Fields 0.59 Ronny Turiaf -0.01 Danilo Gallinari -0.24 Toney Douglas -1.25 Shawne Williams -1.71 Timofey Mozgov -5.95 Bill Walker -6.51 Anthony Randolph -6.51 Roger Mason -8.30 Andy Rautins -13.55 -3.5 is replacement level, so that's a pretty solid looking core there._________________GodismyJudgeOK.com/DStats
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Posted: Sat Dec 25, 2010 12:05 am Post subject:

Traditional Adjusted +/- for less than half of a season is of very limited use by itself but not entirely useless in my opinion. The adjusted +/- at basketballvalue.com is non-regularized and likely over-fit in cases, especially at the extremes, which is where Felton falls in this estimate, and in small sample sizes. Felton's extremely negative rating probably has some significant relationship with Fields' extremely positive rating. Ordinarily I'd be fairly comfortable using the traditional 2 season Adjusted +/- (even though I prefer the regularized and longer term versions) but he was traded and that could change his play and team impact so I'll look further into the current season data. His raw team defensive efficiency on / off is the worst on the team (-9 per 48 minutes) and actually 8th worst in the league among those having played over about 15 minutes per game. His team defensive efficiency while on the court is also tied for the team worst with Amare among those playing more than 10% of team minutes. This is probably a main cause of the poor Adjusted +/-. Felton's 2 season bv.com Adjusted +/- (really about 1.4 seasons) is still quite weak but no where near his extreme 1 year number. It has far lower stated / estimated average error. Whether he eventually ends up the season neutral or positive on 2 season Adjusted +/- like on the previous long timeframe Adjusted +/- ratings or at least a lot less negative or not may come down to how negative his impact on team defense really is this season and how much of the extreme rating is noise / special circumstance / collinearity. The raw +/- shows Felton-Fields-Stoudemire have played 716 minutes together and are +59 for a nice enough average of +4 per 48 minutes. Looking at selective pair data among them and finding the differences between it and the triplet data I find that Felton-Stoudemire on the court without Fields have been -4.4 per 48 minutes in 238 minutes while Fields-Stoudemire without Felton are +21 per 48 minutes in 84 minutes. If you want to think about how good or bad Fields or Felton are respectively using +/- raw or Adjusted, it is worth noting that these specific minutes are having a pretty big impact separating them and so it would be worth reviewing on video of these different sets of minutes and a range of discrete individual and team boxscore stats associated with them to see what detail you can find about what specifically is going on and why it is producing very different scoreboard results- so far. These are very small minute samples and of course might be creating overly extreme impressions that will moderate with time, but some of what is happening might well continue if unexamined and left unchanged It is certainly worth trying to get a handle on rather than just waiting, hoping or ignoring. I haven't done a thorough study... but I can quickly see the offensive and defensive efficiency splits which reveal that Fields-Stoudemire without Felton has shown major improvements on both sides of the court compared to the averages for the trio together while Felton-Stoudemire without Fields slips on both but more so on offense compared to the trio together. Adjusted +/- has limitations, especially on very short-term data on a non-regularized version, but consideration of the current data alongside previous Adjusted +/- estimates and lots of other information can help with creating a decent big picture and helps direct further research (on Felton himself, Felton's impact compared to Fields overall and with and without each other.) Of course the full reality is more complicated. Other teammates need some attention too (especially the weak at SG Douglas and Mason) as do the play calls and the mix of game situations faced by the player combinations (which might be notably different in ways beyond the quality of the other players on the court and beyond what a basic version of Adjusted +/- adjusts for). But raw and Adjusted +/- data can help some in the broad search for a deeper understanding. Felton's relatively good performance on individual boxscore stats is another perspective about his impact, to be considered alongside +/- data. Using one without the other seems less strong / unwise to me. Looking at various splits of that individual data including when the player is in various combinations / lineups with key others probably would help even more. Shot defense is not in simple boxscore based metrics so you either need to look at raw and Adjusted +/- or include counterpart data or both to consider that large element of the game.
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Posted: Sun Dec 26, 2010 2:24 am Post subject:

Has anyone tried to incorporate the changed distance for 3 pointers into any of their studies? It was shorter from 1994-1997 and players like Jordan and a few others may have benefited relative to others
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Posted: Sun Dec 26, 2010 9:01 am Post subject:

Mookie Blaylock got more than half of his career 3-ptrs in this 3-year interval. It also happened to fall in the middle of his career, age 27-29. He had easily his 3 best TS% seasons. But both his PER and his WS/48 were higher the previous year, '93-94, than they were the next 2 years. His career by every measure topped out in '97, and then the 3-pt rug was pulled from under him, and he was in instant decline. Even this extreme example of 3-pt feasting didn't really create his stardom, but just had him shooting more 3's. Jordan, on a smaller scale, also made these short 3's much better. But his PER and WS rates didn't jump appreciably. A rule change, whether a short arc, a hand-check rule, the no-charge circle, is an equal opportunity invitation to adjust your game. Some are more adaptable than others._________________` 36% of all statistics are wrong
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Posted: Sun Dec 26, 2010 12:05 pm Post subject:

Mike G wrote:
Mookie Blaylock got more than half of his career 3-ptrs in this 3-year interval. It also happened to fall in the middle of his career, age 27-29. He had easily his 3 best TS% seasons. But both his PER and his WS/48 were higher the previous year, '93-94, than they were the next 2 years. His career by every measure topped out in '97, and then the 3-pt rug was pulled from under him, and he was in instant decline. Even this extreme example of 3-pt feasting didn't really create his stardom, but just had him shooting more 3's. Jordan, on a smaller scale, also made these short 3's much better. But his PER and WS rates didn't jump appreciably. A rule change, whether a short arc, a hand-check rule, the no-charge circle, is an equal opportunity invitation to adjust your game. Some are more adaptable than others.
The problem I have with simply saying a player's PER etc.. didn't change is that you don't know whether it would have changed under the old rules. It's possible that a favorable rule change prevented a decline. I wholeheartedly agree that great players will attempt to adapt their game to rules changes.
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Posted: Tue Dec 28, 2010 4:32 pm Post subject:

I had to update the primary Advanced SPM spreadsheet because Basketball Reference changed the columns in the team table. I also caught a few minor bugs. Update here: Google Docs That spreadsheet includes ASPM, ASPM projections, salary analysis, single-game predictions, single-game analysis, and player comparisons._________________GodismyJudgeOK.com/DStats
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inkt2002



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Posted: Wed Dec 29, 2010 11:44 am Post subject:

Looks great! Thanks for posting.
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Posted: Thu Dec 30, 2010 10:07 am Post subject:

Crow, By the way, thanks for that detailed analysis.
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Posted: Thu Dec 30, 2010 11:35 am Post subject:

Ok, thanks for the follow-up acknowledgment.


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PostPosted: Tue May 17, 2011 8:36 pm 
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Any plans to release full season ASPM or playoff to date ASPM or NCAA ASPM?

Have any changes to the methodology been considered or made recently?


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PostPosted: Wed May 18, 2011 3:26 pm 
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This spreadsheet has a 1-button update to update to the latest regular season results: https://docs.google.com/leaf?id=0Bx1NfC ... NzQ3&hl=en

It can also be set to run for any year in the past 35 or so and spit out the results.

No updates to the methodology recently. I was kind of limited on what I could do, because I wanted it to be able to work with historical data back to the late 1970s. Limited stats available at that point.

I probably should re-run this doing some of the more advanced calibration I now know how to do, using R. I don't have time right now; I've got some other interesting stuff coming up soon (watch for lineup-level RAPM & Bayesian lineup-level RAPM).

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PostPosted: Wed May 18, 2011 4:55 pm 
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Good that you have the ASPM spreadsheet generally available and capable of going back that far. I would think a summary of just the ASPM values by team at your site would be an attractor.

I'll watch for lineup-level RAPM & Bayesian lineup-level RAPM. They would be welcome advances. A simple full text table at your site or here for say the top 10 lineups by team would be handy and appreciated.


Last edited by Crow on Thu May 19, 2011 6:46 pm, edited 1 time in total.

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PostPosted: Thu May 19, 2011 3:59 pm 
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DSMok1 wrote:
Bayesian lineup-level RAPM

Can you tell us what's Bayesian about it?

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PostPosted: Thu May 19, 2011 6:06 pm 
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I'm going to experiment with different sorts of Bayesian priors (based on different things) to see what gives the best OOS performance. So far, I've done lineup-level RAPM and validated it, but that by its nature regresses toward league average. I want to regress toward a more useful prior to get better OOS performance. I've got several ideas, but I'm not sure what will work and be valid yet. Perhaps toward a regressed team average like your RAPM team ratings. After that, I'll look at something incorporating minutes played or average % of MP by players, etc. Maybe some sort of SPM at some point; I'm not that far along yet.

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PostPosted: Sat Jun 11, 2011 3:11 am 
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Thanks for this! :D

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